Quantum Hall effect in a high-mobility two-dimensional electron gas on a cylindrical surface

We study the quantum Hall effect in a high-mobility, two-dimensional electron gas on a cylindrical surface, where a strong magnetic field gradient is formed along the cross section of the Hall bar. The heterostructure is rolled-up as a single tube and despite the formation of a the new surface the mobility remains high so that the electrons mean free path is as large as the radius of the tube, R = 20 μm. This results in new trajectories, which are bent in space, while being still confined in the quantum well. We show that even for a large magnetic field gradient the Hall resistance shows pronounced plateaus, indicating that the conductance is fully determined by one-dimensional channels corresponding to Landau states including Zeeman splitting. These channels split off the edge into the bulk due to magnetic barriers. We investigate the important case when stripes are formed, for which the magnetic field is oriented nearly 'in-plane'. So called 'snake'-like trajectories with backwards directed velocity exist within these stripes, which do not contribute to the main charge transport